MS has been loosening up on the 4 bits limit and have created a CPP variant of Minecraft which performs better, but they've also introduced their unified login garbage that has almost made me give up Minecraft completely.
The 4-bit stuff is a hangover from Notch doing this (I'd maybe even say a similar-calibre programmer to Chris Sawyer...). The sound has nothing to do with technical limits, that's a post-facto rationalisation.
The game never played midi samples, it was always playing "real" audio. The style was an artistic choice, many similar retro-looking games were using chiptune and the sorts. It's a deliberate juxtaposition...
The CPP variant doesn't really perform better anymore either.
Information about blocks is the overwhelmingly dominant thing being stored in memory for those games, so naturally reducing the size of that data becomes important.